near body predictions at intermediate reynolds...
TRANSCRIPT
Accurate near‐body predictions at intermediate Reynolds numbers
Dr. Gabriel Weymouth, Audrey MaertensSouthampton Marine and Maritime Institute, Southampton
Center for Ocean Engineering, MIT
Hydrodynamic object recognition using pressure sensing
• Blind cave fish use pressure in efficient propulsion, navigation, and predator avoidance
• Applications in autonomous vehicles, harbor safeguarding, energy extraction…
• Re = 2K‐100K
Vorticity of pitching and heaving foil
Mexican tetra
Predictions of near‐field pressure and separation at low angles of attack
Induced change in pressure field passing circular cylinder Can induce separation, but not in this case!
pressure
Fernandez et al MTS 2011
Jump in velocity gradient across boundary causes numerical pressure instability
Griffith & Peskin JCP 2005Muldoon & Acharya IJNM 2008Guy & Hartenstine JCP 2010
wall
flowwall
flow
Problem is exacerbated at higher Reynolds numbers
Problem is exacerbated at higher Reynolds numbers
Obviously, it’s time to throw in the towel
• Switch to cut‐cell method– Sharp interface
–Much more complex
– Stability problems which require lots of numerical trickery to avoid
The smoothing wasn’t the problemLet’s try reformulating the system…The smoothing wasn’t the problemLet’s try reformulating the system…
Coupled two‐domain problem: Fluid system with irregular boundary data
Want one continuous GEQ over the complete domain
Finite kernel convolution of the GEQs unifies the equation domain
Boundary Data Immersion MethodWeymouth & Yue, JCP 2011
Second‐order Taylor expansion simplifies the integrated governing equations
Boundary Data Immersion MethodMaertens & Weymouth, JCP (in review)
Kernel moments are smooth functions of distance to the fluid/body boundary
Never need to explicitly integrate over domains
K
Second‐order BDIM governing equation
• First two terms are “mixed” fluid/body system
• Last term is a correction for discontinuity
• Simple algebraic adjustment to uncoupled fluid system
• Enables (near trivial) Cartesian‐grid method to make excellent predictions
Inclusion of 0 in Poisson equation stabilizes pressure in nonlinear cases
• Enforces correct pressure boundary condition
• Improves pressure conditioning
Inclusion of 0 in Poisson equation stabilizes pressure in nonlinear cases
• Giant cavity remains stable and gives correct pinch‐off
• Simple adjustment ensures robust solution
Bergmann et al PRL 2006
Second‐order term controls shear gradient discontinuity and removes bias
• 1D unsteady channel flow at Re=1000• Both 1st order methods have similar error• 2nd order is improved throughout
Second‐order enables near field predictions on separated foil test case
• SD7003 at 4o AOA, Re=10K– Low curvature foil with fine trailing edge– Very sensitive to IB treatment
Second‐order enables near field predictions on separated foil test case
• Sharp SD7003 at 4o AOA
• Enables analytic treatment of sharp trailing edge
Time‐averaged velocity
magnitude
Second‐order enables near field predictions on separated foil test case
• O(1) method diverges due to pressure instability
• BDIM O(2) matches body‐fitted predictions
* 1st ordero 2nd order
Second‐order at higher Reynolds number
• At Re ~ 25K the flow becomes three‐dimensional at the trailing edge
Spanwise vorticity iso‐contours
Heaving and pitching foil at Re=100K
Leading edge vortex remains
attached
Leading edge vortex remains
attached Tuncer & Platzer 2000
Heaving and pitching foil at Re=100K
• O(2) predicts smooth lift
• Reduces mean drag error from 20% to 5%
Current Status
• BDIM: Analytic convolution GEQ with simple numerical implementations
• First‐order BDIM applies accurate nonlinear pressure BCs
• Second‐order BDIM controls gradient discontinuity at intermediate Re
[email protected] to:Audrey Maertens, Michael Triantafyllou, Dick Yue @ MIT
[email protected] to:Audrey Maertens, Michael Triantafyllou, Dick Yue @ MIT
Future Directions
• Speed‐up through optimizing
• High Re by incorporating BL data
• Continue fun and challenging applications
[email protected] to:Audrey Maertens, Michael Triantafyllou, Dick Yue @ MIT
[email protected] to:Audrey Maertens, Michael Triantafyllou, Dick Yue @ MIT
[email protected] to:Audrey Maertens, Michael Triantafyllou, Dick Yue @ MIT
[email protected] to:Audrey Maertens, Michael Triantafyllou, Dick Yue @ MIT